Aeneid claims Aeneas left Troad and migrated to Italy and a modern book (with no citation) said Aeneas succeed Priam as King of Troy. Can anyone verify or deny latter claim?
There are a few sources that point to a dynasty in the Troad who claimed descent from Aineias. Whether this dynasty actually existed is open to debate, but certainly there are ancient sources that claimed such a dynasty existed, or which were sometimes interpreted that way in antiquity.
(The links for Hellanikos and Demetrios require a subscription, but the text of the fragments there is just taken from Dionysios and Strabo respectively: the pages linked add some commentary.)
Some further reading, with extensive bibliography:
A. Faulkner, The Homeric Hymn to Aphrodite (Oxford, 2008), pp. 3-7
(comes down slightly in favour of a historical dynasty)
S. D. Olson, The Homeric Hymn to Aphrodite and Related Texts (Berlin, 2012), pp. 1-9
(rejects a historical dynasty)
Greco-Roman mythology did not aim at consistency except in the writings of mythographers. Different places had local traditions that would very often be incompatible with the local traditions of other places. In the case of Aineias, the tradition that had him founding a new dynasty in the Troad never took hold outside these few sources; the separate tradition where he emigrated to Italy was obviously much more popular.